If this is really a problem and must be done then I would speak to the hairdresser and see if she can visit, observing very strict rules of hygiene and using protective clothing. You could provide these items. The hairdresser should wear an overall (even a clean man's shirt would do, untouched straight from the wash), a shower cap to completely cover her hair and a face mask. She doesn't need rubber gloves if she washes her hands thoroughly before starting and doesn't touch her face. I don't think a perm would be a good idea as it's too lengthy, just give her an extra short cut. Explain to your mum that is all that can be done and as she won't be going out no-one will see her!
Keep the visit as short as possible. If the hairdresser behaves as if she's in an operating theatre I can't think your mum will be at any risk having her hair cut.